Abstract. A method based on graph theory is investigated for creating global parametrizations for surface triangulations for the purpose of smooth surface fitting. The parametrizations, which are planar triangulations, are the solutions of linear systems based on convex combinations. A particular parametrization, called shape-preserving, is found to lead to visually smooth surface approximations. A standard approach to fitting a smooth parametric curve c(t) through a given sequence of points xi = (xi,yi,zi) ∈ IR 3, i = 1,...,N is to first make a parametrization, a corresponding increasing sequence of parameter values ti. By finding smooth functions x,y,z: [t1,tN] → IR for which x(ti) = xi, y(ti) = yi, z(ti) = zi, an interpolatory curve

We propose a new method to compute planar triangulations of triangulated surfaces for surface parameterization. Our method computes a projection that minimizes the distortion of the surface metric structures (lengths, angles, etc.). It can handle any manifold surface, including surfaces with large curvature gradients and non-convex domain boundaries. We use only the necessary and sufficient constraints for a valid two-dimensional triangulation. As a result, the existence of a theoretical solution to the minimization procedure is guaranteed.

A major challenge facing computer architects today is designing cost-effective hardware that executes multiple operations simultaneously. The goal of such designs is to improve performance by taking advantage of fine-grain parallelism. In this dissertation, I study vector architectures, the oldest of several processor designs that support fine-grain parallelism. Because implementing a cost-effective processor that performs well requires studying not only the design of processors but also the design of algorithms for compilers, this dissertation encompasses aspects of both hardware and software design. In the first half of this dissertation, I demonstrate that a vector architecture is a cost-effective processor that supports fine-grain parallelism. I show that implementing a vector architecture is no more costly than implementing a superscalar architecture, which is currently popular among designers of VLSI microprocessors. I then show that programs that are rich in parallelism tend als...

This paper gives a pathwise construction of Jackson-type queueing networks allowing the derivation of stability and convergence theorems under general probabilistic assumptions on the driving sequences; namely, it is only assumed that the input process, the service sequences and the routing mechanism are jointly stationary and ergodic in a sense that is made precise in the paper. The main tools for these results are the subadditive ergodic theorem, which is used to derive a strong law of large numbers, and basic theorems on monotone stochastic recursive sequences. The techniques which are proposed here apply to other and more general classes of discrete event systems, like Petri nets or GSMP’s. The paper also provides new results on the Jackson-type networks with i.i.d. driving sequences which were studied in the past.

A theoretical approach to construct free form surfaces is presented. We develop the concepts that arise when a free form surface is generated by tracing a mesh, using di#erentiable manifold theory, and generalizing the B-spline scheme. This approach allows to define a family of practical schemes. Four di#erent applications of the generic approach are also presented in this paper.

We propose a new method to compute planar triangulations of faceted surfaces for surface parameterization. In contrast to previous approaches that define the flattening problem as a mapping of the three-dimensional node locations to the plane, our method defines the flattening problem as a constrained optimization problem in terms of angles (only). After applying a scaling that derives from the `curvature' at a node, we minimize the relative deformation of the angles in the plane with respect to their counterparts in the three-dimensional surface. This approach makes the method more stable and robust than previous approaches, which used node locations in their formulations. The new method can handle any manifold surface for which a connected, valid, two-dimensional parameterization exists, including surfaces with large curvature gradients. It does not require the boundary of the flat two-dimensional domain to be predefined or convex. We use only the necessary and sufficient constraints for a valid two-dimensional triangulation. As a result, the existence of a theoretical solution to the minimization procedure is guaranteed.